Question: Simplify the following expression and state the condition under which the simplification is valid. $x = \dfrac{t^2 - 16}{t - 4}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = t$ $ b = \sqrt{16} = -4$ So we can rewrite the expression as: $x = \dfrac{({t} {-4})({t} + {4})} {t - 4} $ We can divide the numerator and denominator by $(t - 4)$ on condition that $t \neq 4$ Therefore $x = t + 4; t \neq 4$